Tables ofJn(ms) are given forn= 0(1)10,s= 1(1)20 andm= 1(1)10 to five decimal places. A second set of tables includesn= 0(1)10,s= 1(1)20 andm= π, 2π, ··· 5π also to five decimal places. These computed values have been arranged in tables with increasingsfor use in the summation of the SchlOmil(lh series which occur in the theory of frequency modulation. The computed values have been checked against existing tables wherever pos